Problem: Solve for $x$ and $y$ using elimination. ${-5x-y = -55}$ ${6x+y = 64}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {-5x-y = -55}\thinspace$ to find $y$ ${-5}{(9)}{ - y = -55}$ $-45-y = -55$ $-45{+45} - y = -55{+45}$ $-y = -10$ $\dfrac{-y}{{-1}} = \dfrac{-10}{{-1}}$ ${y = 10}$ You can also plug ${x = 9}$ into $\thinspace {6x+y = 64}\thinspace$ and get the same answer for $y$ : ${6}{(9)}{ + y = 64}$ ${y = 10}$